Single-exposure High Dynamic Range Imaging (HDRI), as a typical ill-posed problem, has attracted extensive attention from researchers. However, restoration in real-world scenarios has always been an intractable task due to various exposures and noise artifacts. This work proposes an event-based HDRI framework that generalizes to scenes under various exposures by exploiting the high dynamic range of events. To address the challenge of processing diverse exposures, we propose an exposure-aware network incorporating the exposure attention fusion module, which facilitates the adaptive fusion of SDR image and event features. Moreover, the problem of noise in extremely under-exposed regions and events is effectively alleviated by introducing a self-supervised loss, namely EDDN, which effectively enhances the details of saturated areas while simultaneously decreasing noise. We conduct novel event-based HDRI datasets to evaluate our proposed method for benchmarking with diverse exposed images. Comprehensive experiments have demonstrated that our method outperforms the state-of-the-art.